Find unknown probability parameter

2 The probability that Henk goes swimming on any day is 0.2 . On a day when he goes swimming, the probability that Henk has burgers for supper is 0.75 . On a day when he does not go swimming the probability that he has burgers for supper is \(x\). This information is shown on the following tree diagram.
\includegraphics[max width=\textwidth, alt={}, center]{14e8a601-2180-4491-9336-cafd262f2596-2_693_1038_845_555} The probability that Henk has burgers for supper on any day is 0.5 .

1. Find \(x\).
2. Given that Henk has burgers for supper, find the probability that he went swimming that day.

4
\includegraphics[max width=\textwidth, alt={}, center]{c0c7e038-805a-4237-a579-a6571b84f337-2_451_1530_1393_303} A survey is undertaken to investigate how many photos people take on a one-week holiday and also how many times they view past photos. For a randomly chosen person, the probability of taking fewer than 100 photos is \(x\). The probability that these people view past photos at least 3 times is 0.76 . For those who take at least 100 photos, the probability that they view past photos fewer than 3 times is 0.90 . This information is shown in the tree diagram. The probability that a randomly chosen person views past photos fewer than 3 times is 0.801 .

1. Find \(x\).
2. Given that a person views past photos at least 3 times, find the probability that this person takes at least 100 photos.

3 The members of a swimming club are classified either as 'Advanced swimmers' or 'Beginners'. The proportion of members who are male is \(x\), and the proportion of males who are Beginners is 0.7 . The proportion of females who are Advanced swimmers is 0.55 . This information is shown in the tree diagram.
\includegraphics[max width=\textwidth, alt={}, center]{dd75fa20-fead-48d6-aff4-c5e733769f9f-04_435_974_482_587} For a randomly chosen member, the probability of being an Advanced swimmer is the same as the probability of being a Beginner.

1. Find \(x\).
2. Given that a randomly chosen member is an Advanced swimmer, find the probability that the member is male.

5 Over a period of time Julian finds that on long-distance flights he flies economy class on \(82 \%\) of flights. On the rest of the flights he flies first class. When he flies economy class, the probability that he gets a good night's sleep is \(x\). When he flies first class, the probability that he gets a good night's sleep is 0.9 .

1. Draw a fully labelled tree diagram to illustrate this situation. The probability that Julian gets a good night's sleep on a randomly chosen flight is 0.285 .
2. Find the value of \(x\).
3. Given that on a particular flight Julian does not get a good night's sleep, find the probability that he is flying economy class.

1. In a survey, people were asked if they use a computer every day.

Of those people under 50 years old, \(80 \%\) said they use computer every day. Of those people aged 50 or more, \(55 \%\) said they use computer every day. The proportion of people in the survey under 50 years old is \(p\)

1. Draw a tree diagram to represent this information. In the survey, 70\% of all people said they use computer every day.
2. Find the value of \(p\) One person is selected at random. Given that this person uses a computer every day,
3. find the probability that this person is under 50 years old.
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4．The partially completed tree diagram，where \(p\) and \(q\) are probabilities，gives information about Andrew＇s journey to work each day．
\includegraphics[max width=\textwidth, alt={}, center]{7d45bacd-20ac-49b4-8f3f-613edf3739f9-12_661_794_395_511}
\(R\) represents the event that it is raining
W represents the event that Andrew walks to work
\(B\) represents the event that Andrew takes the bus to work
\(C\) represents the event that Andrew cycles to work Given that \(\mathrm { P } ( B ) = 0.26\)
（a）find the value of \(p\) Given also that \(\mathrm { P } \left( R ^ { \prime } \mid W \right) = 0.175\)
（b）find the value of \(q\)
（c）Find the probability that Andrew cycles to work． Given that Andrew did not cycle to work on Friday，
（d）find the probability that it was raining on Friday．